Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves

Details Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves

2011-10-24

arxiv.org/abs/1110.5164v1

Mathematics

Analysis of PDEs

36 pages, 3 figures. Submitted to Amer. J. Math

Scientific paper

In this paper, we shall prove a Carleman estimate for the so-called Zaremba problem. Using some techniques of interpolation and spectral estimates, we deduce a result of stabilization for the wave equation by means of a linear Neumann feedback on the boundary. This extends previous results from the literature: indeed, our logarithmic decay result is obtained while the part where the feedback is applied contacts the boundary zone driven by an homogeneous Dirichlet condition. We also derive a controllability result for the heat equation with the Zaremba boundary condition.

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